Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C3×C4×C5 ⋊ C2×C4 |
| Hall | C3×C5 ⋊ #1898 |
| Sylow | C5 ⋊ #68970 |
| Sylow | C3 ⋊ #10604220 |
1196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^7,3,5|a^2=f,b^2=df,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,i^a=i^3,d^b=dg,f^b=fg,i^b=i^2,h^c=h^2,i^f=i^490 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 27778);